Satan Oscillate My Metallic Sonatas

Malaclypse,
Incorrect. It IS possible to know something about the fixed die:

In this scenario the number '1093' means 'universe that supports life' and all other numbers mean 'universe that doesn't support life'.
Thus God's (the troll's) number generator is very likely to produce the number '1093'...in fact most would concur the probability is 1.


Note: At this point, the classic atheistic position is to ask 'But how can you KNOW that God would probably make a life-friendly universe?'

However, this is simply an argument from ignorance and can easily be countered simply asking 'How do you KNOW that God would NOT make a life-friendly universe?'

Not quite. As stated above...we can know something about the fixed box...it is extremely likely to produce '1093'.


Thoughts and comments welcomed.


Satan Oscillate My Metallic Sonatas

[ February 24, 2002: Message edited by: Satan Oscillate My Metallic Sonatas ]</p>

Satan Oscillate My Metallic Sonatas

Dr Retard,

I believe you misunderstand my objection to your analogy. Let me try to explain.
NOTE:I assume you mean that '1093' is a 'life-friendly universe' and all other numbers represent non life-friendly universes.

I DON'T disagree because RNGs aren't *really* random.
I disagree because you say 'I have a random event...1093 comes up.' The question we are trying to answer is did this life-friendly universe randomly happen? This being the case...your analogy assumes the answer.


I absolutely agree with you! *IF* the universe happened randomly...THEN it is completely absurd to postulate some troll that likes '1093' as an explanation for it.

However, this is the question: 'Did it happen at random?'

As such, a more accurate analogy is the situation in which you have one 'fair' die and one '1093-biased' die. You choose a die (you don't know which) and roll a '1093'.

Now, what die are we looking at? The fair die or the troll's die?


Thoughts and comments welcomed,

Satan Oscillate My Metallic Sonatas

tronvillain

You are claiming to know in advance what the bias of the die is, which is exactly the problem Melaclypse was pointing out.

Tercel

Malaclypse the Younger,
Hmm, your complaints look to me pretty wrong and they seem to get worse as it goes. So I hope you'll excuse me from sounding too much like Koy by the time I get to the end.

Why we would want to find it "suprising" I really don't know, since such is not required for the Fine-Tuning argument unless you're doing the usual stawman of it.

The problem with this objection is that it is simply utterly wrong.

It's not a false argument, but you are correct that such features exist. However the argument ignores them as it should because in their case P(E|D) = P(E|C). They, thus, don't demand design.

Are you SingleDad posting under another name? -No one else I've seen confuses "design" and "caused" and very few other people are capable of translating an argument quite so badly.
You know, you haven't mangaged to get a single premise or conclusion correct in the above. That's impressive.

Is so and do not! The argument is perfectly rigorous becuase the statistics I'm using is the ones which underly Bayes' Theorem: It is Bayes' Theorem in an easier to handle form.

WHAT!?! Okay, this is getting stupid. The two values are not related at all.

Yeah: If we screw with the values we get a screwed result. Big suprise.

Completely false. The Fine-Tuning argument still works if you assume the a priori probability of a designer is orders of magnitude <strong>lower</strong> than the a priori probability of a chance universe (as I demonstrate in my discussion with Dr Retard)

<img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" />
<strong>LOWER</strong>. 12 orders of magnitude lower. Not "higher": lower. LOW - ER.

Tercel

[ February 24, 2002: Message edited by: Tercel ]</p>

Tercel

Malaclypse the Younger,

I do note that one of the weaknesses of the Fine Tuning argument is that we do need to make up two of the values to feed into the formula (P(E|D) and P(D)). I can understand there might be some argument about exactly what value these might take. I'm not particular and I'm happy to use any values within reason for these.

P(E|C) is defined by considering the scientific evidence. You can dispute that if you like I suppose...
That is to say the value of P(E|C) is the whole point of the Fine-Tuning argument. Scientific research has found P(E|C) to have such a low value and that is where the Fine-Tuning argument has developed from.

P(E|D) is: given that an intelligence is creating the universe what is the probability it will create a universe capable of sustaining intelligent life as opposed to a universe incapable of sustaining intelligent life?

<strong>There is no sensible reason to insist that P(E|D) should be as small as P(E|C)!</strong> Indeed common sense would suggest to me that P(E|D) should be greater than 0.5. But certainly there would seem little rational reason to set it too many orders of magnitude lower that that.

P(D), the probability that an intelligent being is responsible for the creation of the universe as opposed to chance does not seem to me to be too improbable a priori. Perhaps 1 in a hundred would seem about right to me. But it hardly matters as the Fine-Tuning argument can cope perfectly with anything above one in a million, million, million, million, million quite easily.

I don't recall using 10^-24 at all.

I readily admit that the probabilities do have to be made up. However it's not a case of pulling any number I feel like out of a hat, these are rational estimates and as such reasoning and common sense play an imporant role. If you have a serious objection or argument against any number I've used your welcome to explain what your disagreement is and what number you think I should be using.
I have absolutely not "carefully constructed" any of these numbers to "prove" my bias.

You keep stating this. Yet you have yet to explain any reason why this statement (which looks to me like a completely random objection) is true.

While you're doing that, please tell me what values you would assign to P(D), P(C) and P(E|D) and why.(Let's keep P(E|C) at 10^-50 since that's a basic scientifically established fact - unless you want to argue with that too?) I will look at your values, explain why I think them reasonable or not: and then I will leave it up to the reader to work out whos values they think are better.

You're confusing P(E|C) with P(C). I'm generously assuming P(C) is <strong>thirty</strong> orders of magnitude more likely than P(D). That is to say I'm generously assuming the probability that an intelligent being created the universe is a million, million, million, million, million times more <strong>unlikely</strong> than the probability that the universe is a result of chance.

P(E|C) and P(D) aren't refering to similar things so can't be compared directly sensibly. You want to try comparing P(C) with P(D) and P(E|C) with P(E|D).

Tercel

Malaclypse the Younger

Tercel

If you could combine Koy's compelling writing style with his excellent grasp of logic, I would admire you indeed.

Note that my italicized comment contains a grammatical error; it should read: "The objective (or at least prior) significance of life has to be established to distingish a priori life-friendly universes to find its occurence "surprising". It is possible that this error has caused you to misunderstand my meaning, so I will simply correct my own remarks.

How so? All distinct sets of physical constants are unique (and presumably each unique set would determine at least one unique feature of the resultant universe). If the argument is that "this universe is unique therefore designed" then that argument would apply to each and every resultant universe.

The chance that the specific arrangement of galaxies we observe arose by chance is very small (and there isn't even any anthropic principle that says we must see the arrangement we do). I can define D such that D is the being who would design the universe with this specific arrangment of galaxies. Clearly P(E|D) = 1 and P(E|C) = 10^whatever. Using your exact same argument, I "conclude" that the particular arrangement of galaxies is "designed".

I can even apply your argument to the specific order of cards in a deck (1/52!), define the designer as that which would produce that specific order of cards, and conclude that every time I shuffle a deck of cards, the resultant order is designed.

To rebut this formulation, you must show that life is "objectively special" (in a way that the arrangements of galaxies or the arrangment of cards is not objectively special, a proposition you seem to explicitly deny.

Despite my best efforts at secrecy, you have found me out. No flies on you.

I don't "confuse" design and cause, I explicitly prefer it because causality is much easier to demonstrate and puts you halfway to design. Design entails causality; if the weaker (causal) version of your argument fails, the stronger (design) version fails along with it.

Few are capable of slinging a gratuitous insult quite so well; your own identity is thus confirmed.

The problem is that you give me so little to work with. The argument you refer to is simply not in any kind of logical form. I do the best I can with what I have, but I am handicapped in my interpretation of your arguments by your lack of logical rigor.

This is not surprising since you did not make a single premise or implication explicit in your argument. I did, however, reproduce your conclusion correctly.

What, are you twelve?

You are using an approximation of (not a "form" of) Bayes' Theorem) which renders (at least this part of) your argument "not entirely rigorous". Please try to pay attention to the precise wording when you're responding.

Ah but they are. I will make the proof more explicit.

E, in this formulation, represents a particular volume in the space of possible constant values. Since both E and the total space is bounded and has finite volume it is possible to divide this space into some finite number of distinct volumes { E1 (our E), E2, ... En }. It is stipulated that n is rather large and thus P(E) is rather small; P(E) is rigorously defined as 1/n.

Now in your forumlation, D is defined in terms of E, (since we are assuming only the improbability of E, not it's objective specialness). Therefore, for each of the alternative spaces (E2 through En) we can define an alternative "designer"; including the original designer we have { D1, D2, ... Dn }.

Since the two sets each have n members, we can conclude that P(D) = P(E). Since P(E|C) = P(E), P(E|D) = 1 (by definition), and P(C) = 1-P(D), we can further conclude that P(C) - P(D) ~= P(E|D) - P(E|C) (for large values of n). Q.E.D.

This should not come as a surprise to you.

I apologize, I misread your your first discussion with Dr. Retard--indeed I was not reading it at all carefully.

In the first response to Dr. Retard you correctly prove that the troll (design) hypothesis is extremely unlikely, although your introduction of P(E|D) = 10^12 is fallacious, since it is stipulated that the troll wants to come up with the particular number. It should be noted that even using P(E|D) = 1, we find that P(E|C) ~= P(E|D) = ~10^12.

However you do not show (as you seem to assert) in the first response that if the probabilities are approximately equal, the FTA argument shows a compelling case for design.

In your second argument, however, the disparity is greater: P(D) = 10^-30 which is indeed 20 orders of magnitude greater than P(E|C) = 10^-50 (-30 is a larger number than -50). The couple of orders of magnitude you offer in the other constants are overwhelmed by this difference. Again you do not show what you assert here, that the FTA argument works with a lower a priori probability of a designer.

Indeed it cannot, according to your approximation since all you're doing is multiplication. You will end up with the same a priori probabilities in the result. The real trick is to rigorously justify your assumptions, not just demonstrate that you can plug arbitrary numbers and get a result.

Again, where you note that the a priori probabilities were substantially the same (where I made the error of interpretation), you correctly note that the FTA fails. In the second instance, where you show the FTA "succeeds", you use a value that is twenty orders of magnitude higher for the a priori probability of a designer.

It should be noted that a "made up" number may be plausible, but it is not, by definition, "reasonable". It is, by definition arbitrary, the opposite of reasonable.

P(E|C) is stipulated to be very small. I don't know it's precise value (or even a rough OOM).

If you define the "intelligence that created the universe" (aka the "designer") in terms of this universe (E), the value of P(E|D) = 1 by definition.

If the "designer" is not defined in terms of this universe, then this number is simply indeterminate. We can make no rational estimate about this number.

By the definition of the probability function P, P(D) represents the a priori probability that the designer exists. If D is defined in terms of E above, then P(D) = P(E) as I prove above. If not, then this value is simply indeterminate.

As noted, this is a purely arbitrary value. To me, about 10^-10000000 "seems" about right, but since humans in general can't cope intuitively with numbers above three, what "seems" right to either of us has little persuasive value.

False. If the a priori probability of the designer is even an order of magnitude less than the a priori probability of the chance existence of this universe, then the FTA fails.

My mistake. You use 10^-12 in your first argument (referring to the specified problem) and 10^-50 in the second argument for the probability of this universe.

As noted, they might be plausible, but they are not at all rational estimates. They are arbitrary guesses. You have not shown that reason comes into play at all.

Sorry, I explained it in a different thread. The full argument appears above.

P(E) = P(E|C) = 10^-50 (stipulated)
P(D) = P(E) (proven above)
P(C) = 1 - P(D) (by definition)
P(E|D) = 1 (stipulated)

Using Bayes theorem (or your approximation),

P(D|E) ~= P(C|E)

I'm confusing nothing. The crux of the bisquit is comparing what is known (or stipulated), with what is assumed. Sure you are giving 30 OOM comparing P(C) to P(D), but you are taking away 48 orders of magnitude comparing P(E|C) with P(E|D). Amazingly enough, you win by 18 OOM.

Do you perhaps work for the IRS?

[ February 24, 2002: Message edited by: Malaclypse the Younger ]</p>

Wizardry

Tercel,

This seems to be a very simple problem. All we are doing is comparing the values

P(E|C)*P(C) and P(E|D)*P(D)

which isn’t really all that difficult considering that P(E|D) and P(C) can both be shown to be trivially close to one. For the purposes of this argument, P(C) is assumed to be equal to the value 1-P(D). Since P(D) is generally assigned a small a priori value, the value of P(C) becomes nearly 1, which makes the first term to be approximately equal to P(E|C).

P(E|D) can be considered to also be trivially close to 1 because the designer in question is defined to prefer a life-sustaining universe to a non-life-sustaining universe. This reduces the second term to approximately P(D).

There are a few objections that can be raised with assigning such a high value to P(E|D). Knowing nothing else about a designer, other than the fact that he is a designer does not necessarily imply that he prefers life to non-life. So arguing from an anonymous designer stand point, the only motivation we have for arguing that P(E|D) is higher than P(E|C) is that E is somehow a preferred condition for a designer. The problem with that is that we are not fully aware of the special phenomena existing in other possible combinations of physical constants, which might also be unique and interesting to a designer.

To better illustrate my point, I am going to refer to the RNG example from the beginning of this thread. An analogous situation to the fine-tuning argument would be to argue that the generated number is a special number, say a prime number or a sum of squares or a product of cubes or a triangular number or some other mathematical anomaly, which receives special attention. Due to this unusual result, it might be concluded by some that the RNG wasn’t truly random because the odds of getting such a special number is so low that there must be some intelligent force which prefers special numbers and contrived to output such a special number. However, the problem with this is that depending on how you look at it, any number might be interesting. The fine-tuning argument seems to me to be resting firmly in a known interesting number like 7 and looking at the other possibilities and remarking on their dullness, in much the same way Hardy lamented the dullness of 1729. Rumanujan was quick to point out however,<a href="http://www.mathpages.com/home/kmath028.htm" target="_blank"> that it is actually quite an interesting number</a>.

For the sake of argument, I will concede a anthropomorphic designer and a value of 1 for P(E|D). Ultimately, this leaves us comparing the values P(E|C) and P(D).

I will first confront the less complicated issue: P(D). This term has the potential of rendering the argument to be rather unconvincing because a convinced theist could assign P(D) a very high value, making the entire argument little more than a confirmatory exercise. Likewise, a staunch atheist could assign P(D) an incredibly low value and render the argument similarly useless. That being said, I find it very difficult, if not impossible, to formulate a reasonable guess for P(D) that would not be pulled from my ass. I couldn’t possibly argue why the value should be 10^-54.32564 rather than 10^-43.89385.

Finally we have P(E|C). I really don’t see how we can reasonably determine a value for this. To my knowledge, we have no evidence concerning possible ranges for these values which would correspond directly to how probable or improbable it was. Sure, life as we know it would be non-existent in a universe where Newton’s constant of gravitation was 30 orders of magnitude greater than its current value, but is that a possible configuration? If experience has taught us anything in science and mathematics, it is that lucky accidents are not really accidents, there is most likely a simpler phenomenon which explains the amazing coincidences. I can not rationally justify assigning any kind of value to P(E|C), even a relative one, because it would be out of ignorance. I don’t even think that modern science has anywhere near the level of sophistication necessary to give us an idea. All they can say is basically “If the constants were different, the universe would be different from the one we observe and would have different phenomena, one of which is probably not life that we are familiar with”, which was obvious already.

The fine-tuning argument seems to boil down to determining which value is greater: P(D) or P(E|C). At this point in time, the answer seems inconclusive, forcing us to rely on other evidence in order to answer the salient question here.

I think we all know which way that evidence points.

Peace out.

tronvillain

Since C and D are not exhaustive, it is not valid to assume P(C)=1-P(D).

HRG

Anyone talking about probabilities (conditional or not) should be aware of the following technical points.

1. It is by no means clear that the space of all possible combination of constants is bounded (compact in the mathematical sense). I'd rather regard it as an open subset of some higher-dimensional Euclidean space.

2. The "volume" of this set is not defined, since we could exchange our "old" constants for "new" ones, as long as there is a (differentiable) one-to-one connection between each "old" and each "new" connections. The famous constants of nature are actually constants of our particular description of nature; if we everywhere replaced the fine-structure constant by its logarithm, physics would not change (only its formulas).

3. Thus all probability distributions on the set of all possible combinations are to some degree arbitrary. Dividing it into equal volumes E1 ... En is thus undefined since the notion of "equal volume" depends on the choice of constants, as in 2.

More specifically, I can rewrite physics in such a way that the tiny speck of constants which allegedly *) is necessary for life as we know it makes up 99% of the total space.

Regards,
HRG.

*) E.g. Victor Stenger claims that many other regions allow life (of a different type) as well.

Malaclypse the Younger

True, but the assumption that P(C) = 1-P(D) is more charitable to the theistic FTA, and the refutation still applies.

However, because of your correct observation, I usually represent D as causal (rather than designed), which makes the interpretation rigorous, and is still charitable to the theistic FTA (since design entails causality).

[ February 25, 2002: Message edited by: Malaclypse the Younger ]</p>